Weaker forms of continuity and vector-valued Riemann integration

M. A. Sofi. "Weaker forms of continuity and vector-valued Riemann integration." Colloquium Mathematicae 129.1 (2012): 1-6. <http://eudml.org/doc/286314>.

@article{M2012,
abstract = {It was proved by Kadets that a weak*-continuous function on [0,1] taking values in the dual of a Banach space X is Riemann-integrable precisely when X is finite-dimensional. In this note, we prove a Fréchet-space analogue of this result by showing that the Riemann integrability holds exactly when the underlying Fréchet space is Montel.},
author = {M. A. Sofi},
journal = {Colloquium Mathematicae},
keywords = {Riemann-integrable function; Fréchet space; weak-convergence},
language = {eng},
number = {1},
pages = {1-6},
title = {Weaker forms of continuity and vector-valued Riemann integration},
url = {http://eudml.org/doc/286314},
volume = {129},
year = {2012},
}

TY - JOUR
AU - M. A. Sofi
TI - Weaker forms of continuity and vector-valued Riemann integration
JO - Colloquium Mathematicae
PY - 2012
VL - 129
IS - 1
SP - 1
EP - 6
AB - It was proved by Kadets that a weak*-continuous function on [0,1] taking values in the dual of a Banach space X is Riemann-integrable precisely when X is finite-dimensional. In this note, we prove a Fréchet-space analogue of this result by showing that the Riemann integrability holds exactly when the underlying Fréchet space is Montel.
LA - eng
KW - Riemann-integrable function; Fréchet space; weak-convergence
UR - http://eudml.org/doc/286314
ER -